The Research Of Several Fused Nonlinear Conjugate Gradient Methods

Nonlinear conjugate gradient algorithm is one of important optimization methods.The iterative process is simple and the required space for storing information is small.Furthermore,it possesses superlinear convergence rate.Due to the rapid development of society and computer technology,solving the large-scale unconstrained optimization problems is becoming widespread.Conjugate gradient method is the top choice for such issues and it receives wide attention of scholars.For years there are various conjugate gradient methods,such as modified methods,scaled methods and fused methods.The paper presents three kinds of fused conjugate gradient algorithms,which are mLS-DY method,PHS-DY method and mHS-CD method.And the mHS-CD algorithm is used to estimate the parameters of auto regressive moving average model.Firstly,the paper introduces six kinds of classical conjugate gradient methods.They are as follows: the FR method;the PRP method;the HS method;the LS method;the CD method and the DY method.And it presents three important forms of fused conjugate gradient algorithms.Besides,the basics of time series modeling are given.Secondly,mLS-DY fused conjugate gradient method with parameters is proposed.By adjusting the values of parameters can not only expand the scope of application but also improve the numerical performance of the presented algorithm.Adding the disturbance factor simplifies the iterative process and accelerates computational efficiency.Under the strong Wolfe line search,the global convergence of mLS-DY method is established.Through a series of numerical experiments,numerical results of the proposed algorithm and NLS-DY algorithm are compared.Thirdly,the paper gives PHS-DY fused conjugate gradient method,which is a convex combination of HS method and DY method.This new algorithm constructs a new formula of search direction.Thus all directions generated in the iterative process are fully reduced and do not depend on any line search technology.The global convergence of PHS-DY method is proved under the generalized Wolfe line search and the numerical experiment shows that the presented algorithm is effective.Finally,in the form of projection,mHS-CD fused conjugate gradient method is obtained.The provided algorithm is global convergent with the normal Wolfe line search and the search direction satisfies the sufficient descent property.Applying mHS-CD method to estimate the parameters improves the fitting effect of autoregressive moving average model.The case analysis indicates that the constructed ARMA model is feasible.